Through 84 undefined slope through58m0 through13 and 34 xint

Through (-8,4), undefined slope through(5,-8),m=0 through(-1,3) and (3,4) x-intercept 3, y-intercept -2 vertical, through (-6,4) horizontal, through (-7,4)

Solution

The equation of a line is y = mx + c where m is the slope and c is the y- intercept.

9. Let the equation of the line be y = mx + c . Since the line passes throgh ( - 8, 4), we have 4 = m(- 8) + c or, - 8m = 4 - c or, m = ( c- 4 ) / 8. Then, the equation of the required line is y = {( c- 4 ) / 8.} + c , where c is the y - intercept of the line.

11 .  Let the equation of the line be y = mx + c. Since m = 0, the equation changes to y = c. Now, since the line passes through ( 5, - 8), we have - 8 = c Thus, the equation of the required line is y = - 8.

13.  Let the equation of the line be y = mx + c. Since the line passes throughthe point ( - 1 , 3) , we have 3 = m( -1) + c or, - m + c = 3...(1). Also, since the line passes through the point(3, 4) , we have 4 = m(3) + c or, 3m + c = 4...(2). Now, on subtracting the 1st equation from the 3rd equation, we get 3m + c - ( - m + c) = 4 - 3 or, 4m = 1 so that m = 1/4. Now, from the 1st equation, we have - 1/4 + c = 3 so that c = 3 + 1/4 = 13/4. Then,. the equation of the required line is y = ( -1/4) x + 13/4.

15. The x- intercept is where y = 0 . Since the x -intercept is 3, the line passes throgh ( 3, 0) . Let the equation of the line be y = mx + c . Here, c is the y -intercept. We are given that c = -2. Then the equation of the line changes to y = mx - 2. Further, since the line passes through ( 3, 0), we have 0 = 3m - 2 or, m = 2/3. Thus, yje equation of the required line is y = (2/3) x - 2.

17.The equation of a vertical line is of the form x = c . Since the line passes through ( - 6, 4), we have - 6 = c . Therefore, the equation of the required line is x = - 6.

19. The equation of a horizontal line is of the form y = c . Since the line passes through ( - 7, 4), we have 4 = c.   Therefore, the equation of the required line is y = 4.